Global semantic typing for inductive and coinductive computing

Inductive and coinductive types are commonly construed as ontological (Church-style) types, denoting canonical data-sets such as natural numbers, lists, and streams. For various purposes, notably the study of programs in the context of global semantics, it is preferable to think of types as semantical properties (Curry-style). Intrinsic theories were introduced in the late 1990s to provide a purely logical framework for reasoning about programs and their semantic types. We extend them here to data given by any combination of inductive and coinductive definitions. This approach is of interest because it fits tightly with syntactic, semantic, and proof theoretic fundamentals of formal logic, with potential applications in implicit computational complexity as well as extraction of programs from proofs. We prove a Canonicity Theorem, showing that the global definition of program typing, via the usual (Tarskian) semantics of first-order logic, agrees with their operational semantics in the intended model. Finally, we show that every intrinsic theory is interpretable in a conservative extension of first-order arithmetic. This means that quantification over infinite data objects does not lead, on its own, to proof-theoretic strength beyond that of Peano Arithmetic. Intrinsic theories are perfectly amenable to formulas-as-types Curry-Howard morphisms, and were used to characterize major computational complexity classes Their extensions described here have similar potential which has already been applied

Is the Mind Massively Modular?

Articl

Existential witness extraction in classical realizability and via a negative translation

We show how to extract existential witnesses from classical proofs using Krivine's classical realizability---where classical proofs are interpreted as lambda-terms with the call/cc control operator. We first recall the basic framework of classical realizability (in classical second-order arithmetic) and show how to extend it with primitive numerals for faster computations. Then we show how to perform witness extraction in this framework, by discussing several techniques depending on the shape of the existential formula. In particular, we show that in the Sigma01-case, Krivine's witness extraction method reduces to Friedman's through a well-suited negative translation to intuitionistic second-order arithmetic. Finally we discuss the advantages of using call/cc rather than a negative translation, especially from the point of view of an implementation.Comment: 52 pages. Accepted in Logical Methods for Computer Science (LMCS), 201

A NASA family of minicomputer systems, Appendix A

This investigation was undertaken to establish sufficient specifications, or standards, for minicomputer hardware and software to provide NASA with realizable economics in quantity purchases, interchangeability of minicomputers, software, storage and peripherals, and a uniformly high quality. The standards will define minicomputer system component types, each specialized to its intended NASA application, in as many levels of capacity as required

Panel discussion: Proposals for improving OCL

During the panel session at the OCL workshop, the OCL community discussed, stimulated by short presentations by OCL experts, potential future extensions and improvements of the OCL. As such, this panel discussion continued the discussion that started at the OCL meeting in Aachen in 2013 and on which we reported in the proceedings of the last year's OCL workshop. This collaborative paper, to which each OCL expert contributed one section, summarises the panel discussion as well as describes the suggestions for further improvements in more detail.Peer ReviewedPostprint (published version